1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 157,722 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 157,712 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      7
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      2
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      3
## 117  2020-06-25          East of England      0
## 118  2020-06-26          East of England      3
## 119  2020-03-01                   London      0
## 120  2020-03-02                   London      0
## 121  2020-03-03                   London      0
## 122  2020-03-04                   London      0
## 123  2020-03-05                   London      0
## 124  2020-03-06                   London      1
## 125  2020-03-07                   London      0
## 126  2020-03-08                   London      0
## 127  2020-03-09                   London      1
## 128  2020-03-10                   London      0
## 129  2020-03-11                   London      6
## 130  2020-03-12                   London      6
## 131  2020-03-13                   London     10
## 132  2020-03-14                   London     14
## 133  2020-03-15                   London     10
## 134  2020-03-16                   London     15
## 135  2020-03-17                   London     23
## 136  2020-03-18                   London     27
## 137  2020-03-19                   London     25
## 138  2020-03-20                   London     44
## 139  2020-03-21                   London     49
## 140  2020-03-22                   London     54
## 141  2020-03-23                   London     63
## 142  2020-03-24                   London     87
## 143  2020-03-25                   London    113
## 144  2020-03-26                   London    129
## 145  2020-03-27                   London    130
## 146  2020-03-28                   London    122
## 147  2020-03-29                   London    146
## 148  2020-03-30                   London    149
## 149  2020-03-31                   London    181
## 150  2020-04-01                   London    202
## 151  2020-04-02                   London    191
## 152  2020-04-03                   London    196
## 153  2020-04-04                   London    230
## 154  2020-04-05                   London    195
## 155  2020-04-06                   London    197
## 156  2020-04-07                   London    220
## 157  2020-04-08                   London    238
## 158  2020-04-09                   London    206
## 159  2020-04-10                   London    170
## 160  2020-04-11                   London    178
## 161  2020-04-12                   London    158
## 162  2020-04-13                   London    166
## 163  2020-04-14                   London    144
## 164  2020-04-15                   London    142
## 165  2020-04-16                   London    139
## 166  2020-04-17                   London    100
## 167  2020-04-18                   London    101
## 168  2020-04-19                   London    103
## 169  2020-04-20                   London     95
## 170  2020-04-21                   London     94
## 171  2020-04-22                   London    109
## 172  2020-04-23                   London     77
## 173  2020-04-24                   London     71
## 174  2020-04-25                   London     58
## 175  2020-04-26                   London     53
## 176  2020-04-27                   London     51
## 177  2020-04-28                   London     43
## 178  2020-04-29                   London     44
## 179  2020-04-30                   London     40
## 180  2020-05-01                   London     41
## 181  2020-05-02                   London     41
## 182  2020-05-03                   London     36
## 183  2020-05-04                   London     30
## 184  2020-05-05                   London     25
## 185  2020-05-06                   London     37
## 186  2020-05-07                   London     37
## 187  2020-05-08                   London     30
## 188  2020-05-09                   London     23
## 189  2020-05-10                   London     26
## 190  2020-05-11                   London     18
## 191  2020-05-12                   London     18
## 192  2020-05-13                   London     16
## 193  2020-05-14                   London     20
## 194  2020-05-15                   London     18
## 195  2020-05-16                   London     14
## 196  2020-05-17                   London     15
## 197  2020-05-18                   London      9
## 198  2020-05-19                   London     14
## 199  2020-05-20                   London     19
## 200  2020-05-21                   London     12
## 201  2020-05-22                   London     10
## 202  2020-05-23                   London      6
## 203  2020-05-24                   London      7
## 204  2020-05-25                   London      9
## 205  2020-05-26                   London     12
## 206  2020-05-27                   London      7
## 207  2020-05-28                   London      8
## 208  2020-05-29                   London      7
## 209  2020-05-30                   London     12
## 210  2020-05-31                   London      6
## 211  2020-06-01                   London     10
## 212  2020-06-02                   London      7
## 213  2020-06-03                   London      6
## 214  2020-06-04                   London      8
## 215  2020-06-05                   London      4
## 216  2020-06-06                   London      0
## 217  2020-06-07                   London      4
## 218  2020-06-08                   London      5
## 219  2020-06-09                   London      4
## 220  2020-06-10                   London      7
## 221  2020-06-11                   London      5
## 222  2020-06-12                   London      3
## 223  2020-06-13                   London      3
## 224  2020-06-14                   London      2
## 225  2020-06-15                   London      1
## 226  2020-06-16                   London      2
## 227  2020-06-17                   London      1
## 228  2020-06-18                   London      2
## 229  2020-06-19                   London      3
## 230  2020-06-20                   London      3
## 231  2020-06-21                   London      4
## 232  2020-06-22                   London      2
## 233  2020-06-23                   London      0
## 234  2020-06-24                   London      3
## 235  2020-06-25                   London      2
## 236  2020-06-26                   London      0
## 237  2020-03-01                 Midlands      0
## 238  2020-03-02                 Midlands      0
## 239  2020-03-03                 Midlands      1
## 240  2020-03-04                 Midlands      0
## 241  2020-03-05                 Midlands      0
## 242  2020-03-06                 Midlands      0
## 243  2020-03-07                 Midlands      0
## 244  2020-03-08                 Midlands      3
## 245  2020-03-09                 Midlands      1
## 246  2020-03-10                 Midlands      0
## 247  2020-03-11                 Midlands      2
## 248  2020-03-12                 Midlands      6
## 249  2020-03-13                 Midlands      5
## 250  2020-03-14                 Midlands      4
## 251  2020-03-15                 Midlands      5
## 252  2020-03-16                 Midlands     11
## 253  2020-03-17                 Midlands      8
## 254  2020-03-18                 Midlands     13
## 255  2020-03-19                 Midlands      8
## 256  2020-03-20                 Midlands     28
## 257  2020-03-21                 Midlands     13
## 258  2020-03-22                 Midlands     31
## 259  2020-03-23                 Midlands     33
## 260  2020-03-24                 Midlands     41
## 261  2020-03-25                 Midlands     48
## 262  2020-03-26                 Midlands     64
## 263  2020-03-27                 Midlands     72
## 264  2020-03-28                 Midlands     89
## 265  2020-03-29                 Midlands     92
## 266  2020-03-30                 Midlands     90
## 267  2020-03-31                 Midlands    123
## 268  2020-04-01                 Midlands    140
## 269  2020-04-02                 Midlands    142
## 270  2020-04-03                 Midlands    124
## 271  2020-04-04                 Midlands    151
## 272  2020-04-05                 Midlands    164
## 273  2020-04-06                 Midlands    140
## 274  2020-04-07                 Midlands    123
## 275  2020-04-08                 Midlands    186
## 276  2020-04-09                 Midlands    139
## 277  2020-04-10                 Midlands    127
## 278  2020-04-11                 Midlands    142
## 279  2020-04-12                 Midlands    139
## 280  2020-04-13                 Midlands    120
## 281  2020-04-14                 Midlands    116
## 282  2020-04-15                 Midlands    147
## 283  2020-04-16                 Midlands    102
## 284  2020-04-17                 Midlands    118
## 285  2020-04-18                 Midlands    115
## 286  2020-04-19                 Midlands     92
## 287  2020-04-20                 Midlands    107
## 288  2020-04-21                 Midlands     86
## 289  2020-04-22                 Midlands     78
## 290  2020-04-23                 Midlands    103
## 291  2020-04-24                 Midlands     79
## 292  2020-04-25                 Midlands     72
## 293  2020-04-26                 Midlands     81
## 294  2020-04-27                 Midlands     74
## 295  2020-04-28                 Midlands     68
## 296  2020-04-29                 Midlands     53
## 297  2020-04-30                 Midlands     56
## 298  2020-05-01                 Midlands     64
## 299  2020-05-02                 Midlands     51
## 300  2020-05-03                 Midlands     52
## 301  2020-05-04                 Midlands     61
## 302  2020-05-05                 Midlands     59
## 303  2020-05-06                 Midlands     59
## 304  2020-05-07                 Midlands     48
## 305  2020-05-08                 Midlands     34
## 306  2020-05-09                 Midlands     37
## 307  2020-05-10                 Midlands     42
## 308  2020-05-11                 Midlands     33
## 309  2020-05-12                 Midlands     45
## 310  2020-05-13                 Midlands     40
## 311  2020-05-14                 Midlands     37
## 312  2020-05-15                 Midlands     40
## 313  2020-05-16                 Midlands     34
## 314  2020-05-17                 Midlands     31
## 315  2020-05-18                 Midlands     34
## 316  2020-05-19                 Midlands     34
## 317  2020-05-20                 Midlands     36
## 318  2020-05-21                 Midlands     32
## 319  2020-05-22                 Midlands     27
## 320  2020-05-23                 Midlands     34
## 321  2020-05-24                 Midlands     19
## 322  2020-05-25                 Midlands     26
## 323  2020-05-26                 Midlands     33
## 324  2020-05-27                 Midlands     29
## 325  2020-05-28                 Midlands     28
## 326  2020-05-29                 Midlands     20
## 327  2020-05-30                 Midlands     20
## 328  2020-05-31                 Midlands     22
## 329  2020-06-01                 Midlands     20
## 330  2020-06-02                 Midlands     22
## 331  2020-06-03                 Midlands     24
## 332  2020-06-04                 Midlands     16
## 333  2020-06-05                 Midlands     21
## 334  2020-06-06                 Midlands     20
## 335  2020-06-07                 Midlands     17
## 336  2020-06-08                 Midlands     16
## 337  2020-06-09                 Midlands     18
## 338  2020-06-10                 Midlands     15
## 339  2020-06-11                 Midlands     13
## 340  2020-06-12                 Midlands     12
## 341  2020-06-13                 Midlands      6
## 342  2020-06-14                 Midlands     17
## 343  2020-06-15                 Midlands     12
## 344  2020-06-16                 Midlands     14
## 345  2020-06-17                 Midlands     10
## 346  2020-06-18                 Midlands     14
## 347  2020-06-19                 Midlands      9
## 348  2020-06-20                 Midlands     13
## 349  2020-06-21                 Midlands     12
## 350  2020-06-22                 Midlands     12
## 351  2020-06-23                 Midlands     12
## 352  2020-06-24                 Midlands     13
## 353  2020-06-25                 Midlands     12
## 354  2020-06-26                 Midlands      1
## 355  2020-03-01 North East and Yorkshire      0
## 356  2020-03-02 North East and Yorkshire      0
## 357  2020-03-03 North East and Yorkshire      0
## 358  2020-03-04 North East and Yorkshire      0
## 359  2020-03-05 North East and Yorkshire      0
## 360  2020-03-06 North East and Yorkshire      0
## 361  2020-03-07 North East and Yorkshire      0
## 362  2020-03-08 North East and Yorkshire      0
## 363  2020-03-09 North East and Yorkshire      0
## 364  2020-03-10 North East and Yorkshire      0
## 365  2020-03-11 North East and Yorkshire      0
## 366  2020-03-12 North East and Yorkshire      0
## 367  2020-03-13 North East and Yorkshire      0
## 368  2020-03-14 North East and Yorkshire      0
## 369  2020-03-15 North East and Yorkshire      2
## 370  2020-03-16 North East and Yorkshire      3
## 371  2020-03-17 North East and Yorkshire      1
## 372  2020-03-18 North East and Yorkshire      2
## 373  2020-03-19 North East and Yorkshire      6
## 374  2020-03-20 North East and Yorkshire      5
## 375  2020-03-21 North East and Yorkshire      6
## 376  2020-03-22 North East and Yorkshire      7
## 377  2020-03-23 North East and Yorkshire      9
## 378  2020-03-24 North East and Yorkshire      8
## 379  2020-03-25 North East and Yorkshire     18
## 380  2020-03-26 North East and Yorkshire     21
## 381  2020-03-27 North East and Yorkshire     28
## 382  2020-03-28 North East and Yorkshire     35
## 383  2020-03-29 North East and Yorkshire     38
## 384  2020-03-30 North East and Yorkshire     64
## 385  2020-03-31 North East and Yorkshire     60
## 386  2020-04-01 North East and Yorkshire     67
## 387  2020-04-02 North East and Yorkshire     74
## 388  2020-04-03 North East and Yorkshire    100
## 389  2020-04-04 North East and Yorkshire    105
## 390  2020-04-05 North East and Yorkshire     92
## 391  2020-04-06 North East and Yorkshire     96
## 392  2020-04-07 North East and Yorkshire    102
## 393  2020-04-08 North East and Yorkshire    107
## 394  2020-04-09 North East and Yorkshire    111
## 395  2020-04-10 North East and Yorkshire    117
## 396  2020-04-11 North East and Yorkshire     98
## 397  2020-04-12 North East and Yorkshire     84
## 398  2020-04-13 North East and Yorkshire     94
## 399  2020-04-14 North East and Yorkshire    107
## 400  2020-04-15 North East and Yorkshire     96
## 401  2020-04-16 North East and Yorkshire    103
## 402  2020-04-17 North East and Yorkshire     88
## 403  2020-04-18 North East and Yorkshire     95
## 404  2020-04-19 North East and Yorkshire     88
## 405  2020-04-20 North East and Yorkshire    100
## 406  2020-04-21 North East and Yorkshire     76
## 407  2020-04-22 North East and Yorkshire     84
## 408  2020-04-23 North East and Yorkshire     63
## 409  2020-04-24 North East and Yorkshire     72
## 410  2020-04-25 North East and Yorkshire     69
## 411  2020-04-26 North East and Yorkshire     65
## 412  2020-04-27 North East and Yorkshire     65
## 413  2020-04-28 North East and Yorkshire     57
## 414  2020-04-29 North East and Yorkshire     69
## 415  2020-04-30 North East and Yorkshire     57
## 416  2020-05-01 North East and Yorkshire     64
## 417  2020-05-02 North East and Yorkshire     48
## 418  2020-05-03 North East and Yorkshire     40
## 419  2020-05-04 North East and Yorkshire     49
## 420  2020-05-05 North East and Yorkshire     40
## 421  2020-05-06 North East and Yorkshire     51
## 422  2020-05-07 North East and Yorkshire     45
## 423  2020-05-08 North East and Yorkshire     42
## 424  2020-05-09 North East and Yorkshire     44
## 425  2020-05-10 North East and Yorkshire     40
## 426  2020-05-11 North East and Yorkshire     29
## 427  2020-05-12 North East and Yorkshire     27
## 428  2020-05-13 North East and Yorkshire     28
## 429  2020-05-14 North East and Yorkshire     31
## 430  2020-05-15 North East and Yorkshire     32
## 431  2020-05-16 North East and Yorkshire     35
## 432  2020-05-17 North East and Yorkshire     26
## 433  2020-05-18 North East and Yorkshire     30
## 434  2020-05-19 North East and Yorkshire     27
## 435  2020-05-20 North East and Yorkshire     22
## 436  2020-05-21 North East and Yorkshire     33
## 437  2020-05-22 North East and Yorkshire     22
## 438  2020-05-23 North East and Yorkshire     18
## 439  2020-05-24 North East and Yorkshire     26
## 440  2020-05-25 North East and Yorkshire     21
## 441  2020-05-26 North East and Yorkshire     21
## 442  2020-05-27 North East and Yorkshire     22
## 443  2020-05-28 North East and Yorkshire     21
## 444  2020-05-29 North East and Yorkshire     25
## 445  2020-05-30 North East and Yorkshire     20
## 446  2020-05-31 North East and Yorkshire     20
## 447  2020-06-01 North East and Yorkshire     16
## 448  2020-06-02 North East and Yorkshire     23
## 449  2020-06-03 North East and Yorkshire     23
## 450  2020-06-04 North East and Yorkshire     17
## 451  2020-06-05 North East and Yorkshire     18
## 452  2020-06-06 North East and Yorkshire     21
## 453  2020-06-07 North East and Yorkshire     14
## 454  2020-06-08 North East and Yorkshire     11
## 455  2020-06-09 North East and Yorkshire     12
## 456  2020-06-10 North East and Yorkshire     18
## 457  2020-06-11 North East and Yorkshire      7
## 458  2020-06-12 North East and Yorkshire      9
## 459  2020-06-13 North East and Yorkshire     10
## 460  2020-06-14 North East and Yorkshire     11
## 461  2020-06-15 North East and Yorkshire      8
## 462  2020-06-16 North East and Yorkshire     10
## 463  2020-06-17 North East and Yorkshire      9
## 464  2020-06-18 North East and Yorkshire     10
## 465  2020-06-19 North East and Yorkshire      6
## 466  2020-06-20 North East and Yorkshire      4
## 467  2020-06-21 North East and Yorkshire      4
## 468  2020-06-22 North East and Yorkshire      6
## 469  2020-06-23 North East and Yorkshire      7
## 470  2020-06-24 North East and Yorkshire      7
## 471  2020-06-25 North East and Yorkshire      3
## 472  2020-06-26 North East and Yorkshire      1
## 473  2020-03-01               North West      0
## 474  2020-03-02               North West      0
## 475  2020-03-03               North West      0
## 476  2020-03-04               North West      0
## 477  2020-03-05               North West      1
## 478  2020-03-06               North West      0
## 479  2020-03-07               North West      0
## 480  2020-03-08               North West      1
## 481  2020-03-09               North West      0
## 482  2020-03-10               North West      0
## 483  2020-03-11               North West      0
## 484  2020-03-12               North West      2
## 485  2020-03-13               North West      3
## 486  2020-03-14               North West      1
## 487  2020-03-15               North West      4
## 488  2020-03-16               North West      2
## 489  2020-03-17               North West      4
## 490  2020-03-18               North West      6
## 491  2020-03-19               North West      7
## 492  2020-03-20               North West     10
## 493  2020-03-21               North West     11
## 494  2020-03-22               North West     13
## 495  2020-03-23               North West     15
## 496  2020-03-24               North West     21
## 497  2020-03-25               North West     21
## 498  2020-03-26               North West     29
## 499  2020-03-27               North West     35
## 500  2020-03-28               North West     28
## 501  2020-03-29               North West     46
## 502  2020-03-30               North West     67
## 503  2020-03-31               North West     52
## 504  2020-04-01               North West     86
## 505  2020-04-02               North West     96
## 506  2020-04-03               North West     95
## 507  2020-04-04               North West     98
## 508  2020-04-05               North West    102
## 509  2020-04-06               North West    100
## 510  2020-04-07               North West    135
## 511  2020-04-08               North West    127
## 512  2020-04-09               North West    119
## 513  2020-04-10               North West    117
## 514  2020-04-11               North West    138
## 515  2020-04-12               North West    125
## 516  2020-04-13               North West    129
## 517  2020-04-14               North West    131
## 518  2020-04-15               North West    114
## 519  2020-04-16               North West    135
## 520  2020-04-17               North West     98
## 521  2020-04-18               North West    113
## 522  2020-04-19               North West     71
## 523  2020-04-20               North West     83
## 524  2020-04-21               North West     76
## 525  2020-04-22               North West     86
## 526  2020-04-23               North West     85
## 527  2020-04-24               North West     66
## 528  2020-04-25               North West     65
## 529  2020-04-26               North West     55
## 530  2020-04-27               North West     54
## 531  2020-04-28               North West     57
## 532  2020-04-29               North West     62
## 533  2020-04-30               North West     59
## 534  2020-05-01               North West     45
## 535  2020-05-02               North West     56
## 536  2020-05-03               North West     55
## 537  2020-05-04               North West     48
## 538  2020-05-05               North West     48
## 539  2020-05-06               North West     44
## 540  2020-05-07               North West     49
## 541  2020-05-08               North West     42
## 542  2020-05-09               North West     30
## 543  2020-05-10               North West     41
## 544  2020-05-11               North West     35
## 545  2020-05-12               North West     38
## 546  2020-05-13               North West     25
## 547  2020-05-14               North West     26
## 548  2020-05-15               North West     33
## 549  2020-05-16               North West     32
## 550  2020-05-17               North West     24
## 551  2020-05-18               North West     31
## 552  2020-05-19               North West     35
## 553  2020-05-20               North West     27
## 554  2020-05-21               North West     27
## 555  2020-05-22               North West     26
## 556  2020-05-23               North West     31
## 557  2020-05-24               North West     26
## 558  2020-05-25               North West     31
## 559  2020-05-26               North West     27
## 560  2020-05-27               North West     27
## 561  2020-05-28               North West     28
## 562  2020-05-29               North West     20
## 563  2020-05-30               North West     19
## 564  2020-05-31               North West     13
## 565  2020-06-01               North West     12
## 566  2020-06-02               North West     27
## 567  2020-06-03               North West     22
## 568  2020-06-04               North West     22
## 569  2020-06-05               North West     16
## 570  2020-06-06               North West     26
## 571  2020-06-07               North West     20
## 572  2020-06-08               North West     20
## 573  2020-06-09               North West     16
## 574  2020-06-10               North West     16
## 575  2020-06-11               North West     16
## 576  2020-06-12               North West     11
## 577  2020-06-13               North West      9
## 578  2020-06-14               North West     15
## 579  2020-06-15               North West     15
## 580  2020-06-16               North West     13
## 581  2020-06-17               North West     10
## 582  2020-06-18               North West     13
## 583  2020-06-19               North West      7
## 584  2020-06-20               North West     11
## 585  2020-06-21               North West      6
## 586  2020-06-22               North West     10
## 587  2020-06-23               North West     13
## 588  2020-06-24               North West     13
## 589  2020-06-25               North West     11
## 590  2020-06-26               North West      2
## 591  2020-03-01               South East      0
## 592  2020-03-02               South East      0
## 593  2020-03-03               South East      1
## 594  2020-03-04               South East      0
## 595  2020-03-05               South East      1
## 596  2020-03-06               South East      0
## 597  2020-03-07               South East      0
## 598  2020-03-08               South East      1
## 599  2020-03-09               South East      1
## 600  2020-03-10               South East      1
## 601  2020-03-11               South East      1
## 602  2020-03-12               South East      0
## 603  2020-03-13               South East      1
## 604  2020-03-14               South East      1
## 605  2020-03-15               South East      5
## 606  2020-03-16               South East      8
## 607  2020-03-17               South East      7
## 608  2020-03-18               South East     10
## 609  2020-03-19               South East      9
## 610  2020-03-20               South East     13
## 611  2020-03-21               South East      7
## 612  2020-03-22               South East     25
## 613  2020-03-23               South East     20
## 614  2020-03-24               South East     22
## 615  2020-03-25               South East     29
## 616  2020-03-26               South East     35
## 617  2020-03-27               South East     34
## 618  2020-03-28               South East     36
## 619  2020-03-29               South East     55
## 620  2020-03-30               South East     58
## 621  2020-03-31               South East     65
## 622  2020-04-01               South East     66
## 623  2020-04-02               South East     55
## 624  2020-04-03               South East     72
## 625  2020-04-04               South East     80
## 626  2020-04-05               South East     82
## 627  2020-04-06               South East     88
## 628  2020-04-07               South East    100
## 629  2020-04-08               South East     83
## 630  2020-04-09               South East    104
## 631  2020-04-10               South East     88
## 632  2020-04-11               South East     88
## 633  2020-04-12               South East     88
## 634  2020-04-13               South East     84
## 635  2020-04-14               South East     65
## 636  2020-04-15               South East     72
## 637  2020-04-16               South East     56
## 638  2020-04-17               South East     86
## 639  2020-04-18               South East     57
## 640  2020-04-19               South East     70
## 641  2020-04-20               South East     87
## 642  2020-04-21               South East     51
## 643  2020-04-22               South East     54
## 644  2020-04-23               South East     57
## 645  2020-04-24               South East     64
## 646  2020-04-25               South East     51
## 647  2020-04-26               South East     51
## 648  2020-04-27               South East     40
## 649  2020-04-28               South East     40
## 650  2020-04-29               South East     47
## 651  2020-04-30               South East     29
## 652  2020-05-01               South East     37
## 653  2020-05-02               South East     36
## 654  2020-05-03               South East     17
## 655  2020-05-04               South East     35
## 656  2020-05-05               South East     29
## 657  2020-05-06               South East     25
## 658  2020-05-07               South East     27
## 659  2020-05-08               South East     26
## 660  2020-05-09               South East     28
## 661  2020-05-10               South East     19
## 662  2020-05-11               South East     25
## 663  2020-05-12               South East     27
## 664  2020-05-13               South East     18
## 665  2020-05-14               South East     32
## 666  2020-05-15               South East     24
## 667  2020-05-16               South East     22
## 668  2020-05-17               South East     18
## 669  2020-05-18               South East     22
## 670  2020-05-19               South East     12
## 671  2020-05-20               South East     22
## 672  2020-05-21               South East     15
## 673  2020-05-22               South East     17
## 674  2020-05-23               South East     21
## 675  2020-05-24               South East     17
## 676  2020-05-25               South East     13
## 677  2020-05-26               South East     19
## 678  2020-05-27               South East     18
## 679  2020-05-28               South East     12
## 680  2020-05-29               South East     21
## 681  2020-05-30               South East      8
## 682  2020-05-31               South East     12
## 683  2020-06-01               South East     11
## 684  2020-06-02               South East     13
## 685  2020-06-03               South East     17
## 686  2020-06-04               South East     11
## 687  2020-06-05               South East     11
## 688  2020-06-06               South East     10
## 689  2020-06-07               South East     12
## 690  2020-06-08               South East      8
## 691  2020-06-09               South East     10
## 692  2020-06-10               South East     11
## 693  2020-06-11               South East      5
## 694  2020-06-12               South East      6
## 695  2020-06-13               South East      6
## 696  2020-06-14               South East      7
## 697  2020-06-15               South East      7
## 698  2020-06-16               South East     11
## 699  2020-06-17               South East      8
## 700  2020-06-18               South East      4
## 701  2020-06-19               South East      6
## 702  2020-06-20               South East      5
## 703  2020-06-21               South East      3
## 704  2020-06-22               South East      2
## 705  2020-06-23               South East      8
## 706  2020-06-24               South East      6
## 707  2020-06-25               South East      4
## 708  2020-06-26               South East      2
## 709  2020-03-01               South West      0
## 710  2020-03-02               South West      0
## 711  2020-03-03               South West      0
## 712  2020-03-04               South West      0
## 713  2020-03-05               South West      0
## 714  2020-03-06               South West      0
## 715  2020-03-07               South West      0
## 716  2020-03-08               South West      0
## 717  2020-03-09               South West      0
## 718  2020-03-10               South West      0
## 719  2020-03-11               South West      1
## 720  2020-03-12               South West      0
## 721  2020-03-13               South West      0
## 722  2020-03-14               South West      1
## 723  2020-03-15               South West      0
## 724  2020-03-16               South West      0
## 725  2020-03-17               South West      2
## 726  2020-03-18               South West      2
## 727  2020-03-19               South West      4
## 728  2020-03-20               South West      3
## 729  2020-03-21               South West      6
## 730  2020-03-22               South West      7
## 731  2020-03-23               South West      8
## 732  2020-03-24               South West      7
## 733  2020-03-25               South West      9
## 734  2020-03-26               South West     11
## 735  2020-03-27               South West     13
## 736  2020-03-28               South West     21
## 737  2020-03-29               South West     18
## 738  2020-03-30               South West     23
## 739  2020-03-31               South West     23
## 740  2020-04-01               South West     22
## 741  2020-04-02               South West     23
## 742  2020-04-03               South West     30
## 743  2020-04-04               South West     42
## 744  2020-04-05               South West     32
## 745  2020-04-06               South West     34
## 746  2020-04-07               South West     39
## 747  2020-04-08               South West     47
## 748  2020-04-09               South West     24
## 749  2020-04-10               South West     46
## 750  2020-04-11               South West     43
## 751  2020-04-12               South West     23
## 752  2020-04-13               South West     27
## 753  2020-04-14               South West     24
## 754  2020-04-15               South West     32
## 755  2020-04-16               South West     29
## 756  2020-04-17               South West     33
## 757  2020-04-18               South West     25
## 758  2020-04-19               South West     31
## 759  2020-04-20               South West     26
## 760  2020-04-21               South West     26
## 761  2020-04-22               South West     23
## 762  2020-04-23               South West     17
## 763  2020-04-24               South West     19
## 764  2020-04-25               South West     15
## 765  2020-04-26               South West     27
## 766  2020-04-27               South West     13
## 767  2020-04-28               South West     17
## 768  2020-04-29               South West     15
## 769  2020-04-30               South West     26
## 770  2020-05-01               South West      6
## 771  2020-05-02               South West      7
## 772  2020-05-03               South West     10
## 773  2020-05-04               South West     17
## 774  2020-05-05               South West     14
## 775  2020-05-06               South West     19
## 776  2020-05-07               South West     16
## 777  2020-05-08               South West      6
## 778  2020-05-09               South West     11
## 779  2020-05-10               South West      5
## 780  2020-05-11               South West      8
## 781  2020-05-12               South West      7
## 782  2020-05-13               South West      7
## 783  2020-05-14               South West      6
## 784  2020-05-15               South West      4
## 785  2020-05-16               South West      4
## 786  2020-05-17               South West      6
## 787  2020-05-18               South West      4
## 788  2020-05-19               South West      6
## 789  2020-05-20               South West      1
## 790  2020-05-21               South West      9
## 791  2020-05-22               South West      6
## 792  2020-05-23               South West      6
## 793  2020-05-24               South West      3
## 794  2020-05-25               South West      8
## 795  2020-05-26               South West     11
## 796  2020-05-27               South West      5
## 797  2020-05-28               South West     10
## 798  2020-05-29               South West      7
## 799  2020-05-30               South West      3
## 800  2020-05-31               South West      2
## 801  2020-06-01               South West      7
## 802  2020-06-02               South West      2
## 803  2020-06-03               South West      7
## 804  2020-06-04               South West      2
## 805  2020-06-05               South West      2
## 806  2020-06-06               South West      1
## 807  2020-06-07               South West      3
## 808  2020-06-08               South West      3
## 809  2020-06-09               South West      0
## 810  2020-06-10               South West      1
## 811  2020-06-11               South West      2
## 812  2020-06-12               South West      2
## 813  2020-06-13               South West      2
## 814  2020-06-14               South West      0
## 815  2020-06-15               South West      1
## 816  2020-06-16               South West      2
## 817  2020-06-17               South West      0
## 818  2020-06-18               South West      0
## 819  2020-06-19               South West      0
## 820  2020-06-20               South West      2
## 821  2020-06-21               South West      0
## 822  2020-06-22               South West      1
## 823  2020-06-23               South West      1
## 824  2020-06-24               South West      1
## 825  2020-06-25               South West      0
## 826  2020-06-26               South West      1

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-25"

The completion date of the NHS Pathways data is Thursday 25 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -10.4786   -3.2020   -0.3888    3.6233    5.9215  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.848e+00  5.477e-02   88.52   <2e-16 ***
## note_lag    1.245e-05  5.581e-07   22.30   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 13.83783)
## 
##     Null deviance: 7335.7  on 56  degrees of freedom
## Residual deviance:  786.7  on 55  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  127.474937    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 114.352477 141.739949
## note_lag      1.000011   1.000014

Rsq(lag_mod)
## [1] 0.8927576

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1710.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.0    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_4.0.2     knitr_1.29       
## [13] jsonlite_1.7.0    broom_0.5.6       dbplyr_1.4.4      compiler_4.0.2   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_4.0.2      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-148      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.15         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.6     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-25      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-41   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-80    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-12   abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_4.0.2        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0